| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Simpson's rule application |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing basic C3 content. Part (a) requires simple recall that ln(6x)=0 when x=1/6. Part (b) is routine differentiation of ln(6x) giving 1/x. Part (c) is a standard Simpson's rule application with clearly specified strips—purely procedural calculation with no problem-solving insight required. All parts are below average difficulty for A-level. |
| Spec | 1.06d Natural logarithm: ln(x) function and properties1.07l Derivative of ln(x): and related functions1.09f Trapezium rule: numerical integration |
The diagram shows the curve with equation $y = \ln(6x)$.
\includegraphics{figure_1}
\begin{enumerate}[label=(\alph*)]
\item State the $x$-coordinate of the point of intersection of the curve with the $x$-axis. [1]
\item Find $\frac{dy}{dx}$. [2]
\item Use Simpson's rule with 6 strips (7 ordinates) to find an estimate for $\int_1^7 \ln(6x) \, dx$, giving your answer to three significant figures. [4]
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2011 Q1 [7]}}